On families of quadratic surfaces having fixed intersections with two hyperplanes

We investigate families of quadrics all of which have the same intersection with two given hyperplanes. The cases when the two hyperplanes are parallel and when they are nonparallel are discussed. We show that these families can be described with only one parameter and describe how the quadrics are transformed as the parameter changes. This research was motivated by an application in mixed integer conic optimization. In that application, we aimed to characterize the convex hull of the union of the intersections of an ellipsoid with two half-spaces arising from the imposition of a linear disjunction.     

Production of Organometallic Polymers by the Interfacial Technique. XXXII. Reaction Variables in the Synthesis of Oligomeric Tin Poly(cobalticinium Esters) and Thermal Properties of the Products

The synthesis of oligomeric tin poly(cobalticinium esters) is presented as a function of the particular reaction variables stirring rate, pH and amount of added base, mole ratio of reactants, concentration of reactants, and volume of organic phase. Factors which decrease the solubility of the stannane apparently act to increase the yield of polyester. The thermal characterization of I was carried out via DSC and TGA. The products generally exhibit endotherms below 150 to 200[ddot]C which may be related to T_g. Above 200[ddot]C, degradation occurs in air by an oxidative mode.